I have auditory processing disorder.
For me, it meant that I had difficulty with phonics. There are certain sounds that I don't perceive at all. My reading skills are visual in nature. I can recognize entire words almost as if they were word pictures. When they are broken apart into sounds, they become meaningless to me.
Also, I can't do the thing that is called "selective listening." If I am in a noisy place with multiple conversations, I cannot tune out the background noise to listen to the person who is speaking to me. It all sounds as if it is at the same volume (excessively loud).
Although I sometimes seem as if I have hearing loss, that is not true. My hearing is better than normal. I just can't filter out anything at all so I respond to everything or I get a monster sized headache and have to get away before I start responding like a wild animal!
Oddly enough, however, my auditory processing problems have not affected whatever part of the brain is responsible for understanding music. I have had dreams in four-part harmony and my thoughts are frequently musical. If school had been sung, I would have been a very happy camper.
As for brain dominance, I don't know what all of this means. I am not a visual thinker. I think in melody and harmony and rhythm. But I learn with the help of music and art!